In hoping to reduce the amount of threads asking 'Wheres the hunter?' and 'where can I get the Hotknife?' I have decided to make a guide to some of the vehicles you can unlock, without using cheats. There is now an added section for other vehicles which don't quite fit into this category.

The Hunter (the apache army helicopter) -
All gold at plane school: Hunter at verdant meadows.
Complete all story missions: Hunter at naval base.
The hunter is also the helicopter used in the helicopter checkpoint collection race 'Heli Hell.' Simply fly it to your hangar and cancel the race.

The SWAT (the SWAT tank, shoots water) -
You drive one during the LAST mission of the game (End of the Line). Instead of doing what you're supposed to do with it, drive it to your garage and park it in there. Fail the mission by killing yourself... but make sure the SWAT has stayed in the garage before completing the mission.
Another way to get the SWAT is after you get it for the mission drive to the inport/export dock in SF. Now pick it up with the crane and lower it into the water. You will fail the mission because the game thinks the tank was destroyed. You can then take it out of the water and drive it to a garage. (Thanks to m52nickerson).

The Hydra (harrier Jet) -
Spawns at Verdant Meadows after you complete the mission 'Vertical Bird' for Toreno.
Spawns inside the restricted area after you complete the mission 'Vertical Bird' for Toreno.
Spawns inside the aircraft carrier in the Naval Base after you complete the mission 'Vertical Bird' for Toreno.
Spawns on top of Sweet's house, in Grove Street, after successfully completing 100% of the game (mission progress: 100%).

The Rhino (the tank) -
Spawns inside the resticted area.
Steal one when you are on a 6 star wanted level.
Spawns underneath the bridge, on Grove Street, after successfully completing 100% of the game (mission progress: 100%).

The Hotknife (really fast really cool car) -
All gold in Driving School. The license plate will always be 'GOLD.' This is one sweet car.

The Hotring Racer (rally car from Vice City) -
Successfully complete '8 Track' at the Los Santos Stadium. The Monster Truck will also spawn after completing this mission.

The Bloodring Banger (the car you use in Blood Ring) -
Successfully complete Blood Ring in the San Fierro Stadium.

The Sandking (best offroad vehicle IMO) -
Found underneath that giant Satellite Dish at The Ear in the Desert.

The News Chopper (the san andreas news helicopter) -
You can steal one during the Las Venturas Airport Checkpoint race 'Whirly-Bird Waypoint.' Simply start the race, land it in your hangar, get out, let the hangar close and fail the race.

The Predator (police boat) -
Spawns inside the naval base. You really can't do much with this boat.

The Dumper and The Dozer (heavy vehicles) -
At the bottom of the quarry after you complete the Quarry missions.

The Monster (monster truck) -
Get 50% progress with girlfriend Michelle. It will spawn whenever she is available for a date, outside her garage.
Complete '8 Track'.
Also at the trailer park that's opposite that suicidal ped - across the bridge from Santa Maria Beach.

The AT400 (jumbo jet) -
Spawns inside the large hangar inside the Las Venturas airport. I am under the impression it will only spawn after completing Flying School, although some people have mentioned it spawning there [inside the hangar] at any point during the game.

The Phoenix (cool sports car from Vice City) -
You can steal one during the race 'San Fierro Hills' in the San Fierro Street Racing. Simply park it in your garage, get out, let the garage close and fail the race.

The Stuntplane (crazy plane that you can do tricks with) -
All silver, or better, at plane school. All bronze will unlock the Rustler.
This is also the plane used in the checkpoint collection race 'Barnstorming.'

Police Maverick (police helicopter) -
On the roof of the police station in Pershing Square, of Los Santos.

NOT UNLOCKABLE VEHICLESbut included in this guide nontheless

The FBI Truck (the FBI truck) -
Can only be spawned using CHEAT DEVICES such as ARMAX. I am only mentioning this in the guide because so many people ask how do you get this vehicle.

The Andromada (an aeroplane) -
Can only be spawned using CHEAT DEVICES such as ARMAX. I am only mentioning this in the guide because so many people ask how do you get this vehicle.

The Lawn Mower (mows lawns IRL, not in San Andreas though) -
Go to your Vinewood safe house... once there, go east and look for a house that has a winding driveway. Once there, go to the top to find the Lawn Mower.

The Broadway (lowrider, required for Pimping missions) -
There is one parked in a gas station in Los Santos. There is also one near Madd Dogg's crib.

Cropduster (crop plane) -
On a hill at the Panopticon. If you fly over the hill that is east of the airport, you should see a little shed, and a Cropduster.
Also spawns on a small dirt airstrip in bone county next to a small house - just east of the quarry by a an oil field, Las Venturas.

The Euros (required for import/export) -
Go to the Camels Toe, Las Venturas... the car is parked right under the sphinx statue, in front of the doors. It may take a few minutes of driving back and forth from this area to make it spawn. Note that it will only spawn if it's currently on the import/export list.

The Patriot (required for import/export) -
Spawns in Easter Basin military base at the end of the dock.
Can be found in the Restricted Area.

*****
This is the end of this guide. I will add more if I can think of any I've missed, and if you think you can spot any mistakes, please refer me to them and I'll double check, and if neccessary, edit this post.

Originally posted by Ace_Roller
Yes, there are two unlockable monsters:
1) complete the 8-track and it will appear outside the stadium
2)The one at Michelle's house. You get it after getting 50% of progress with her